US10128652B2 - Stabilizing a DC electricity network - Google Patents
Stabilizing a DC electricity network Download PDFInfo
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- US10128652B2 US10128652B2 US14/344,760 US201214344760A US10128652B2 US 10128652 B2 US10128652 B2 US 10128652B2 US 201214344760 A US201214344760 A US 201214344760A US 10128652 B2 US10128652 B2 US 10128652B2
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J1/00—Circuit arrangements for dc mains or dc distribution networks
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60R—VEHICLES, VEHICLE FITTINGS, OR VEHICLE PARTS, NOT OTHERWISE PROVIDED FOR
- B60R16/00—Electric or fluid circuits specially adapted for vehicles and not otherwise provided for; Arrangement of elements of electric or fluid circuits specially adapted for vehicles and not otherwise provided for
- B60R16/02—Electric or fluid circuits specially adapted for vehicles and not otherwise provided for; Arrangement of elements of electric or fluid circuits specially adapted for vehicles and not otherwise provided for electric constitutive elements
- B60R16/03—Electric or fluid circuits specially adapted for vehicles and not otherwise provided for; Arrangement of elements of electric or fluid circuits specially adapted for vehicles and not otherwise provided for electric constitutive elements for supply of electrical power to vehicle subsystems or for
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J1/00—Circuit arrangements for dc mains or dc distribution networks
- H02J1/14—Balancing the load in a network
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
- H03H7/01—Frequency selective two-port networks
- H03H7/0138—Electrical filters or coupling circuits
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
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- Y02E40/34—
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- Y10T307/43—
Definitions
- the invention relates to a method of stabilizing a direct current (DC) electricity network or subnetwork having a DC voltage bus, for example a high voltage direct current (HVDC) network or subnetwork.
- DC direct current
- HVDC high voltage direct current
- the network may be found on board transport means such as an aircraft or a road vehicle or it may power a building such as a factory.
- subnetwork is used to mean a local network forming part of a larger electricity network.
- a DC network or subnetwork typically comprises a DC voltage source powering a plurality of electrical loads, such as converters (e.g. of the type comprising an inverter, an actuator, a storage source (a supercapacitor), a permanent magnet synchronous machine, etc.), which loads are connected in parallel to the terminals of the voltage source and each of which is to receive a current or power setpoint.
- converters e.g. of the type comprising an inverter, an actuator, a storage source (a supercapacitor), a permanent magnet synchronous machine, etc.
- Each load may thus correspond to a different piece of equipment and need not necessarily have any communications link with the other loads, possibly having its own independent active load control.
- a DC network or subnetwork differs from a distributed AC network by the increased importance of the constraint associated with ensuring that the DC network and its loads are stable.
- the loads together with the network itself should normally be dimensioned so that their respective impedances enable a stable network to be obtained.
- a DC network is unstable at an operating point if the voltage or current signal at the terminals of its load oscillate with an amplitude that increases over time.
- Passive stabilization of a load of a network consists in dimensioning its impedance so as to satisfy the stability criteria of the network. This leads to significant overdimensioning of passive elements (resistors and capacitors) in the network so as to enable the network to be stable under various configurations. That solution is not always satisfactory since it can lead to an increase in the size and the weight of the network, where that constitutes a major problem when the network is to be an on-board network, in particular in an aircraft. Furthermore, it is possible that such overdimensioning does not comply with certain initially specified constraints, such as a cutoff frequency of a filter, for example. Furthermore, adding a load to such a network that is stabilized in passive manner can lead to the network becoming unstable, even if the load added to the network is itself stable.
- Another passive technique for stabilizing a network is to ensure that the loads do not consume more than a certain amount of power from the network, by incorporating saturations for the reference setpoints of the load.
- Active stabilization of the load on a dedicated network consists in modifying its control setpoint in order to increase the stability of the network. Nevertheless, that solution is limited since it applies to a simple network having only one load.
- the article “Active stabilization of a poorly damped input filter supplying a constant power load” by Awan et al., in Proc. ECCE' 09 describes a method of actively stabilizing a load of a network, proposing specific state feedback based on the circle criterion. It is also known to stabilize a network having a plurality of loads in centralized manner. The network then has a stabilization member that acquires information about the entire network and that generates a vector containing stabilizing signals for each of the loads, thereby stabilizing the network as a whole.
- a particular object of the invention is to avoid those drawbacks in a manner that is simple, effective, and inexpensive.
- the invention provides an active and decentralized stabilization method for a DC network or subnetwork.
- the invention provides a method of stabilizing a DC electricity network, the network having a DC voltage source powering electrical loads that are connected in parallel to the terminals of the voltage source and each of which is to receive a current or voltage setpoint, the method being characterized in that the network is stabilized by regulating the setpoints applied to the loads by means of a virtual stabilization impedance generated at the terminals of each load, these virtual impedances being dimensioned so as to stabilize the network at various desired operating points and in various given configurations of the network including the state in which at least one load is inactive or has failed and the state in which the stabilization of a load is inactive, each virtual impedance being generated by means of a non-linear regulation loop acting on the setpoint for the corresponding load.
- C v represents a virtual capacitance and K is a correction coefficient equivalent to 1/R, 1/K thus representing a virtual resistance.
- C v and K are thus parameters defining the virtual impedance generated at the terminals of the load.
- the DC network is stabilized by a decentralized approach by putting a multiblock stabilization system into place.
- the principle of this approach is to use a decentralized structure to put a multi-block stabilization system into place on the DC network.
- the system is made up of a plurality of independent local stabilization blocks installed on each load of the system. In this way, it is possible to damp the system in front of each load, thereby locally limiting sources of instability. This makes it possible to stabilize the network as a whole.
- the decentralized aspect of this approach contributes to making the system reliable.
- Each stabilization block is independent of the others and is arranged locally in the network, there being no need for any connections between them, and a failure of any one of them does not affect the others. Furthermore, it is possible to dimension the set of blocks in such a manner as to guarantee that the system remains stable under certain failure scenarios.
- each regulation loop uses a non-linear regulation relationship generating an output signal of the type K.f(x), where x is a control variable for the load and K is a correction coefficient specific to the load, the correction coefficients (K 1 , K 2 , . . . , K n ) being determined by performing the steps consisting in:
- the method of the invention makes it possible to ensure that a DC network or subnetwork is stabilized by stabilizing the loads of the network or subnetwork, and does so for defined operating points regardless of the configuration and/or the failures of the network.
- the stabilizing of each load takes account of the impact of each load on the stabilization of the network overall.
- the method of the invention makes it possible to avoid overdimensioning the passive elements of the network or to overdimension them to a small extent only by creating a virtual impedance (e.g. a capacitance or a resistance) upstream from each load, thereby enabling the loads to be stabilized and also enabling the overall network to be stabilized.
- a virtual impedance e.g. a capacitance or a resistance
- this virtual impedance is to damp disturbances that might be generated on the network or at the terminals of the load, and it is “dimensioned” in such a manner as to stabilize the network at its various desired operating points, in the various given network configurations, and in the event of at least one load failing (i.e. the load being deactivated or breaking down).
- the virtual impedance generated at the terminals of each load is obtained by regulating the control setpoint of the load by means of a non-linear relationship and a predetermined correction coefficient.
- the vector comprising the optimum correction coefficient for all of the loads is determined so that the above-mentioned constraints are satisfied and a target function can be achieved.
- step a) may consist in defining a non-linear model of the network and in linearizing it around an operating point or in expressing its Jacobean.
- the constraints to be satisfied in step b) may comprise acceptable ranges of values for the correction coefficients and for maintaining stabilization in the event of the network being reconfigured, in the event of a failure in the stabilization of at least one load, and given variations or inaccuracies in the parametric values specific to the network.
- the mathematical model includes equations characterizing the network in the absence of one or more loads and/or in the absence of stabilization for one or more loads.
- the stabilization is thus robust against breakdowns and reconfigurations of the network without identifying the configuration in real time and without modifying the regulation/stabilization parameters used.
- the optimization algorithm used in step c) may serve to compare the calculation of the target function using a vector with the calculation of the same function using another vector in which the correction coefficients are the smallest possible, and then in repeating these steps until the vector under consideration minimizes the defined target function.
- This is selected in such a manner as to direct efforts for stabilizing the network in the manner desired by a designer (e.g. minimal for actuators, maximal for storage sources). It is possible to use any algorithm for optimization under constraints (genetic, gradient method, etc.).
- the present invention also provides a DC type electricity network comprising a voltage source powering electrical loads that are connected in parallel to the terminals of the voltage source, each of which is designed to receive a current or power setpoint, the network being characterized in that each load is stabilized by regulating its setpoint by means of a stabilization block having an input connected to means for measuring the voltage at the terminals of the load and an output connected to a terminal for applying the load setpoint via a summing circuit that is also connected to means for issuing a setpoint.
- a local stabilization block is installed in the regulation loop of each load.
- the fact that the load has a plurality of stabilization blocks that are local leads to a reduction in the cabling needed for transmitting information (measurements, stabilizing signal reference) compared with incorporating a single stabilization block in the network (for centralized stabilization), which block would then need to be connected to a large number of sensors for delivering all of the measurements to the block.
- Incorporating local stabilization blocks in the network also makes it possible to reduce the number of sensors involved since only the voltages at the terminals of the loads are needed.
- the stabilization block extracts the high frequency component of the voltage, i.e. it must filter out its DC component.
- the filtering may be performed with the help of a lowpass filter and a subtracter, the input of the filter being connected to the above-mentioned measurement means and its output being connected to a subtracter that is for subtracting the filter output signal from the signal coming from the measurement means.
- a subtracter that is for subtracting the filter output signal from the signal coming from the measurement means.
- each virtual impedance is generated by a converter powering the load (such as an inverter, a buck circuit, a boost circuit, . . . ) by means of a stabilization block that generates non-linear state feedback and that is forwarded to the converter by being superposed on the setpoint of the corresponding load.
- a converter powering the load such as an inverter, a buck circuit, a boost circuit, . . .
- a stabilization block that generates non-linear state feedback and that is forwarded to the converter by being superposed on the setpoint of the corresponding load.
- increasing the parameter C v or K and increasing the stabilization signal serves to raise the threshold for the maximum power that can be consumed by the load from the network and guarantees stability for the interaction between the load and the network.
- the above-defined mathematical model of the electricity network can then be provided with stabilizing state feedback.
- the invention also provides transport means such as an aircraft, characterized in that they include a stabilized electricity network as described above.
- FIG. 1 shows a layout for a DC electricity network having a DC voltage source and three loads
- FIG. 2 shows a simplified DC electricity network having a voltage source and a single load that is stabilized actively by creating a virtual impedance Z at its terminals;
- FIG. 3 shows a DC electricity network similar to that of FIG. 1 and comprising three local stabilization blocks for creating virtual impedances for stabilizing the loads;
- FIGS. 4 a and 4 b show respective blocks for stabilizing a load of a DC network
- FIGS. 5 and 6 are block diagrams showing the steps of the method of the invention.
- FIG. 7 is a graph showing how the DC bus voltage varies for the three loads of the FIG. 1 network in response to a power step, when the three loads are not stabilized.
- FIGS. 8 and 9 are graphs showing how the DC bus voltage varies for the three loads of the FIG. 3 network in response to a power step, when the three loads are stabilized as shown in FIG. 8 , and when only two of the loads are stabilized, with the stabilizing function of one of the loads having failed in the example of FIG. 9 .
- FIG. 1 shows a DC electricity network 10 suitable for fitting on board transport means such as an aircraft, the network having a DC voltage source 11 with output terminals that are connected in parallel to the input terminals of three different loads.
- the first load 12 comprises a permanent magnet synchronous machine 14 (PMSM) powered by a three-phase inverter 16 with torque control via a conventional d-q vector control.
- PMSM permanent magnet synchronous machine
- the second load 18 comprises a DC/DC converter 20 powering a single resistance 22 , the unit being power regulated so that this provides a load that consumes well-controlled power from the network.
- the third load 24 is a super capacitor (SC) that is connected to the network via another DC/DC converter 26 that is electrically bidirectional.
- SC super capacitor
- the unit is also power regulated. It is thus possible to control exchanges of power between the SC and the network.
- the voltage of the DC bus is v n and the voltages at the terminals of the three loads are respectively v 1 , v 2 , and v n .
- the DC network or subnetwork of the invention may for example be a unit of the electrical brake actuation controller (EBAC) type, an electrical landing gear system (ELS) subnetwork, or an electrical flight control system (EFCS), a primary distribution unit of the Primes type, etc.
- EBAC electrical brake actuation controller
- ELS electrical landing gear system
- EFCS electrical flight control system
- the loads of the network 10 are servo-controlled sufficiently well for it to be possible to assume that they operate at constant power.
- the input voltage V e is also assumed to be perfectly constant.
- the stability of a load may be studied individually before dealing with the situation when all three loads are connected to the network simultaneously.
- the stability of each load may be studied by studying the Nyquist frequency plots of the open loop transfer functions (OLTFs) of the systems for configurations in cascade (one load).
- the stability of the overall network is assessed by studying the zeros of the denominator of a transfer function, which, for each load, is the transfer function of the ratio of the voltage v s across the terminals of the load (v 1 , v 2 , or v n ) over the input voltage V e (v s /V e ). The results obtained may be confirmed by simulation, as explained below.
- the electrical configurations of the networks may be unstable if the control setpoint (e.g. power) for the loads exceeds a certain threshold.
- This power limit is defined by the structure of the network and by its content, i.e. by the values of the parameters that make it up.
- passive elements such as capacitors, resistors, or inductors vary as a function of several parameters that are not always controllable and/or constant.
- consideration may be given to temperature variations or to aging, which act on the electrical properties of the systems. This thus leads to a change to the stability properties of the system that might lead to a state of instability.
- the invention proposes defining appropriate commands that generate “stabilizing” signals that are superposed on the reference setpoints for the loads and that thus make it possible to guarantee complete stability for the system or to improve the stability of the system. These signals are advantageously zero under steady conditions in order to avoid disturbing or modifying the setpoints desired by a user or an original operating point.
- the method of the invention makes it possible to overdimension the passive elements of the network to a smaller extent or not at all by creating a virtual impedance Z (capacitance, resistance, etc.) upstream from each load, thereby enabling the loads and the network as a whole to be stabilized ( FIG. 2 ).
- the purpose of this virtual impedance is to damp any disturbances that might be generated on the network or at the terminals of the load, and it is “dimensioned” in such a manner as to stabilize the network at the various desired operating points in the various given network configurations, and in the event of at least one of the loads failing (i.e. being deactivated or breaking down).
- the stabilizing impedance for each load is generated by a stabilization block 28 ( FIG. 3 ) that acts directly on the setpoint loop of the load in order to control the setpoint and provide stability, in particular by:
- the stabilization block 28 of FIG. 4 a serves to generate a virtual resistance at the terminals of a load.
- the block 28 comprises voltage multiplier means 30 for multiplying the voltage v s as measured across the terminals of the load by a gain or a correction coefficient K (equivalent to 1/R) that is directly proportional to the amplitude of the stabilizing signal, in order to produce a signal U.
- the input of a lowpass filter 32 having a cutoff frequency w c is connected to the output of the means 30 , and therefore receives the signal U.
- the output signal X 3 from the filter 32 is subtracted from the signal U by means of a subtracter 34 .
- the output signal P v from the subtracter 34 is added to the setpoint signal P s0 of the load by a summing circuit 36 having its output connected to the load.
- the cutoff angular frequency w c is dimensioned so that only voltage variations are seen by the local stabilizers, the DC components being eliminated.
- the numerical value selected must incorporate the fact that all of the frequencies adjacent to the resonant frequencies generated by the interconnection filters of the network as a whole must be capable of being taken into account by each local stabilization block.
- the variant embodiment of the stabilization block 28 ′ shown in FIG. 4 b serves to generate a virtual capacitance C v across the terminals of a load.
- This block 28 ′ also comprises a lowpass filter 32 having a cutoff frequency w c that receives as input the DC bus voltage v s and that provides an output that is written v slf .
- a subtracter 34 serves to subtract the filtered signal v slf from the signal v s .
- the output signal from the subtracter 34 corresponds to a high frequency oscillation that is multiplied by the angular frequency of the lowpass filter by multiplier means 35 of gain w c .
- the output signal from the means 35 and the signal v slf are transmitted to additional multiplier means 37 to produce a regulated power signal p v as a function of the virtual capacitance C v that is to be generated at the terminals of the load.
- L f represents an inductance, i.e. represents the current delivered by the voltage source V e
- r f represents a resistance
- v s represents the voltage across the terminals of the load
- v e represents the voltage
- C or C f represents a capacitance that together with the inductance L f forms an LC filter.
- v s0 is the voltage across the terminals of the load for the operating point under consideration.
- P s0max When the power setpoint (P s0 ) of the load reaches P s0max , the load is no longer stable.
- P s0max thus represents a threshold that must not be reached by the setpoint P s0 .
- P s0max is directly proportional to the capacitance C. Increasing this capacitance, by adding an additional virtual capacitance to the terminals of the load makes it possible to increase the threshold P s0max .
- the model incorporates a filtered derivative of the measurement of the DC bus voltage (v s ), this model being of the following type:
- v slf V e + V e 2 + 4 ⁇ p s ⁇ ⁇ 0 ⁇ r f 2 ( 6 ) and in which, for a first order filter, v slf is an additional state variable.
- the above-mentioned state variables x 1 , x 2 , and x 3 are functions of measurable physical parameters of the network or of network data.
- K is the correction coefficient (1/K represents a virtual resistance, K being equivalent to 1/R) to be defined for stabilizing the load:
- the determination of the parameters K depends in particular on the architecture of the network and on the number of active loads in the network. These parameters are determined firstly by solving the set of matrices that define a network, and secondly as a function of the various desired operating points, the various possible configurations, and criteria for minimizing the influence of dynamic performance on the loads.
- the stabilization relationship incorporates damping of the signal and takes account of the fact that undamped oscillations should disappear. Because this damping is necessary only around an operating point, it may be followed by a suitable filter, e.g. a lowpass filter, as shown in FIGS. 4 a and 4 b.
- a suitable filter e.g. a lowpass filter
- the network of FIG. 3 is modelled and linearized at a given operating point.
- This network corresponds to the network of FIG. 1 with stabilization blocks of the invention added thereto, each block serving to regulate the control setpoint for the load with which it is associated in such a manner as to stabilize it within the network.
- the linear mathematical model of the DC network may be defined by the following matrix (M sound ) in which the parameters K 1 , K 2 , and K sc represent respectively the correction coefficients of the first, second, and third load.
- a target function is determined for stabilizing the network as a function of constraints that are described in greater detail below.
- This target function may be expressed by the following equation:
- constraints serve to guarantee stability for the system. They are imposed on the real parts of the eigenvalues ⁇ of the state matrices of the system in its various configurations. The constraints are valid locally around an operating point, and the stability of all of the operating points corresponding to a domain D given by two power ranges is investigated, the ranges being defined by the following relationship:
- the following matrix M failure1 is a mathematical model of the network in the event of one branch of the first load being open, e.g. at the point O 1 in FIG. 3 .
- Linearizing the system makes it possible to define the eigenvalues of the system by acting on the various values of K, the real parts of each pole being made negative (which guarantees stability in the domain close to the linearization point), and are advantageously made to be less than ⁇ 5 in order to increase the robustness margins of the system.
- FIG. 5 is a highly diagrammatic representation of the steps of the method of the invention for determining correction coefficients that are applied to the setpoints of the loads in order to stabilize them within the DC network. This figure shows the constraints that may be taken into account for defining the correction coefficients.
- the network model as established above serves to define the target function that is to be minimized and to assess the impact of each load on stabilization (block 68 ).
- Modeling the network, its operating points, and its desired acceptable degraded modes makes it possible to define a set of equations enabling a single set of values to be defined for the coefficients (K 1 to K n ).
- the advantage of such a unique solution is that it enables the defined values to be robust and unique for all the desired situations that are taken into account in the modeling and in the system of equations.
- the calculation and optimization algorithm is not specific and may for example be the Matlab fmincon function which solves and optimizes the set of equations. This makes it possible to define values for the above-mentioned correction coefficients K.
- the target of decentralized or multi-block stabilization is to provide coherent dimensioning of the stabilization blocks so as to ensure that the system is stable in a plurality of circumstances.
- use is made of a method of optimization under constraints. With such an approach, it is possible to take account of constraints on the stability of the system. By way of example, these may be robustness margins, tolerance to failures of the stabilizers, and managing possible reconfigurations of the system in the event of a failure in one of the loads of the network.
- constraints on the stability of the system may be robustness margins, tolerance to failures of the stabilizers, and managing possible reconfigurations of the system in the event of a failure in one of the loads of the network.
- use is made of a relationship associating all of the stabilization blocks with their impact on their respective loads.
- the advantage of the presently-proposed method lies in defining the problem. It is then solved with the help of whatever algorithm is selected for optimization under constraints.
- the method used is the Matlab fmincon function available in the “optimization toolbox”. It is based on minimizing the target function to which the weighted coefficient constraints are added. The coefficients weighting the constraints ensure that the minimum of the new function as defined in this way cannot correspond to solutions that do not satisfy the constraints.
- the optimization is based on the linear models (M sound , M failure1 , M failuresc , and M failure2 ) corresponding to the various possible scenarios in the above-described scenario.
- the impedances are determined by defining and solving a problem of optimization under constraints.
- the impedances are the solution to the problem of optimization under constraints. They correspond to the coefficients K and Cv.
- FIG. 6 shows diagrammatically the steps of the optimization method of the invention.
- a user begins by determining a domain D in which the correction coefficients K are to be determined.
- the optimization algorithm defines a vector X 0 in this domain, which vector comprises a set of load correction coefficients (block 80 ).
- the optimization algorithm begins by verifying that all of the above-mentioned constraints are satisfied for the vector X 0 (block 82 ). If the constraints are not satisfied, the algorithm defines a new vector ( 84 , 80 ).
- the algorithm calculates the target function with the vector X 0 (block 86 ) and then compares the results obtained with a result for the same function when the vector used is as small as possible, i.e. when the correction coefficients that make it up are as small as possible (block 88 ). If the target (or “objective”) function f obj (X 0 ) is greater than or equal to f obj (X min ) (branches 90 , 84 ), then the algorithm calculates a new vector and reiterates the steps of blocks 80 , 82 , and 86 .
- the main step consists in obtaining the coefficient values K that satisfy the constraints that have been set.
- the above-defined problem of optimization under constraints has been adapted to the formatting requested by the Matlab fmincon function, as set out below:
- X fmincon(f min , x 0 , A, B, A eq , b eq , x min , x max , NL con )
- x min and x max definition ranges for x
- NL con non-linear constraints
- the vectors x min and x max define the maximum and minimum values that can be taken by the coefficients K.
- the value of the virtual resistance (corresponding to 1/K) is set to lie in the range infinite (no damping) to 1.
- the robustness margin (RM) is taken to be equal to 5.
- 1
- the load 1 must therefore perform the major part of stabilization, and it is this that sets the value of the coefficient K 1 .
- the other coefficients it can be seen that they decrease as the value of r opt is lowered.
- FIG. 7 is a graph showing how the DC bus voltage (v 1 , v 2 , and v n ) varies on the three loads of the FIG. 1 network in response to a power step, when the three loads are not stabilized. It can be seen that following the power step, the oscillations of the signals do not stabilize. On the contrary, their amplitudes increase. When the eigenvalues of the transfer function v n /V e for each load are studied, it is found that at least some of the zeros of the denominator of the transfer function have a positive real part, thereby demonstrating the instability of the system.
- FIG. 8 is a graph showing how the DC bus voltage (v 1 , v 2 , and v n ) on the three loads of the FIG. 1 network varies in response to a power step, when the three loads are stabilized by the method of the invention. Unlike the preceding figure, the oscillations in the signals stabilize and their amplitudes decrease over time, in responses to a power step. The DC network is thus stabilized.
- FIG. 9 is a graph corresponding to FIG. 8 , but in which the stabilization block for the load SC has failed and no longer performs stabilization. It can still be seen that the oscillations of the signals stabilize and that their amplitudes diminish over time in response to a power step. The DC network thus remains stabilized in spite of one of the stabilization blocks being deactivated.
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Abstract
Description
p v(t)=v s(t)·C v ·dv s /dt
or
p v(t)=K·v s 2 −X 3
where vs represents the voltage at the terminals of the load, Cv and K are parameters defining the virtual stabilization impedance, and X3 is the output signal from a filter of cutoff frequency wc that receives the signal K.vs 2 as input,
-
- increasing the parameter C, or K and increasing the stabilization signal, serves to raise the threshold of the setpoint of the load or the threshold of the maximum power consumed by the load, and guarantees stability of the network.
p v(t)=v s(t)·C v ·dv s /dt
or
p v(t)=K·v s 2 −X 3
in which vs represents the voltage at the terminals of the power converter controlling the load, Cv and K are parameters defining the virtual stabilization impedance, and X3 is the output signal from a filter having a cutoff frequency wc that receives the signal K.vs 2 as input,
-
- adjusting variations in the setpoint between the various requested operating points;
- ensuring that the network is stable when at least one of the stabilization blocks is no longer active; and
- ensuring that the network is stable when at least one of the loads is disconnected (network reconfiguration).
where Lf represents an inductance, i.e. represents the current delivered by the voltage source Ve, rf represents a resistance, vs represents the voltage across the terminals of the load, ve represents the voltage, C or Cf represents a capacitance that together with the inductance Lf forms an LC filter.
where vs0 is the voltage across the terminals of the load for the operating point under consideration.
where Cv is the virtual capacitance generated upstream from the load by the stabilization block and iv is the current passing through the capacitance.
with the following parameters for the operating point (is0, vs0):
and in which, for a first order filter, vslf is an additional state variable.
U=K·v s 2 and p v(t)=v s 2 −X 3
(cf.
with this being done for the following circumstances:
The following matrix Mfailure2 is a mathematical model of the network in the event of a branch of the second load being open, e.g. at point O2 in
The following matrix Mfailuresc is a mathematical model of the network in the event of a branch of the third load being open, e.g. at point O3 in
In order to incorporate a robustness criterion, the real parts of the eigenvalues of the matrices Msound, Mfailure1, Mfailuresc, and Mfailure2 are required to be less than a strictly negative value written RM. This provides a safety margin for taking account of possible variations or inaccuracies in the parameter values. Finally, the constraints to be satisfied are given by the following relationship:
x0=[0.05 0.05 0.05]t
The robustness margin (RM) is taken to be equal to 5.
f min, (K 1 , K 2 , K sc)=−|a sc |K sc +|a 1|(K 1 +K 2) |a sc|+2|a 1|=1
Claims (9)
p v(t)=v s(t)·C v ·dv s /dt
or
p v(t)=K·v s 2 −X 3
p v(t)=v s(t)·C v ·dv s /dt
or
p v(t)=K·v s 2 −X 3
p v(t)=v s(t)·C v ·dv s /dt
p v(t)=K·v s 2 −X 3
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PCT/FR2012/052037 WO2013038105A1 (en) | 2011-09-14 | 2012-09-12 | Stabilization of a dc electric network |
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